1. Field of the Invention
The present invention relates to modeling wellbores in reservoir simulation, and more particularly to generating unconstrained Voronoi grids in a domain containing complex internal boundaries.
2. Description of the Related Art
Reservoir simulation is the primary tool used by the oil industry for the planning and development of subterranean hydrocarbon reservoirs. With the advancement of drilling technology, wellbores which have multiple branches and complex geometries are increasingly being deployed in order to enhance production and injection processes in these reservoirs.
Applicant's related prior co-pending U.S. patent application Ser. No. 14/171,815 mentioned above relates to accurately modeling near-wellbore flow for complex wells to enhance the performance prediction for these wells. The modeling allows reservoir analysts and engineers improved data about wells and reservoirs for the decision making process to exploit the available resources.
A Corner-point-geometry or CPG grid is a known and often used to represent faults in reservoir simulation models. An example of a CPG grid is shown at G in FIG. 2. A CPG grid is a flexible, structured grid in which each finite-volume cell is a hexahedron defined by its eight-corner coordinates. For a severely faulted model, the grid can become severely distorted and non-orthogonal. A technique known as multi-point flux approximation (MPFA) is normally required to maintain discretization accuracy. However, numerical difficulties can be caused for an iterative linear solver when solving the multiphase flow problems using discretization in this manner. In practice, only major faults are represented so that the grid is not too distorted.
Unstructured gridding around internal boundaries has also been done. So far as is known, unstructured gridding for the most part has used what is known as Delaunay triangulation, with what is known as a Voronoi grid being the dual grid of the generated triangular mesh.
Traditionally, in order to preserve the internal boundary geometry, the applied Delaunay triangulation has to be constrained in order to honor internal boundary lines as the generated triangle's edge. This technique is described U.S. Pat. No. 8,212,814, “Generation of a Constrained Voronoi Grid in a Plane”, Branets et al. During the constrained Delaunay triangulation of this technique, unstructured grid points have to be adjusted, repositioned or removed, or new grid points have to be inserted explicitly near the internal boundary in order to satisfy the constraint criteria to have the generated near-internal-boundary triangles have edges on the internal boundary. Such a grid point adjustment procedure is called grid smoothing. It is usually computationally expensive, especially for large simulation models. Additionally, it leads to congested grid regions in order to satisfy boundaries but at the cost of lessened discretization, and less satisfactory convergence for reservoir simulation.
In the prior art, in the near intersection area, the grid points from each of the internal boundaries were kept during Delaunay triangulation which in turn could create many bad shaped triangles with small angles. This is discussed in “Modeling Heavily Faulted Reservoirs,” SPE paper 48998, SPE Annual Technical Conference and Exhibition, New Orleans, La., USA, Sep. 27-30, 1998, Heinemann, et al. As a consequence, such undesired triangles increased modeling complexity and introduced numerical errors which eventually led to poor discretization and poor computational efficiency during flow simulation.
The prior art constrained Voronoi grid generation used a constrained method which involved grid smoothing to force the generated Voronoi cell edge to conform to the internal boundary geometry. The grid smoothing had to swap triangle edges, re-position grid points, or insert a new point in order to preserve the internal boundary geometry structure.